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arXiv · 1910.13281

Geometric Flows of Curves, Two-Component Camassa-Holm Equation and Generalized Heisenberg Ferromagnet Equation

Aigul Taishiyeva·Tolkynay Myrzakul·Gulgassyl Nugmanova·Shynaray Myrzakul·Kuralay Yesmakhanova·Ratbay Myrzakulov
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Abstract

In this paper, we study the generalized Heisenberg ferromagnet equation, namely, the M-CVI equation. This equation is integrable. The integrable motion of the space curves induced by the M-CVI equation is presented. Using this result, the Lakshmanan (geometrical) equivalence between the M-CVI equation and the two-component Camassa-Holm equation is established. Note that these equations are gauge equivalent each to other.

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Aigul Taishiyeva, Tolkynay Myrzakul, Gulgassyl Nugmanova, Shynaray Myrzakul, Kuralay Yesmakhanova, Ratbay Myrzakulov. 2019-10-28. Geometric Flows of Curves, Two-Component Camassa-Holm Equation and Generalized Heisenberg Ferromagnet Equation. https://arxiv.org/abs/1910.13281

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